Higher-order optimality conditions for set-valued optimization

DOI10.1007/s10957-007-9345-3zbMath1149.49020OpenAlexW2139548281MaRDI QIDQ933824

Kok Lay Teo, Sheng Jie Li, Xiao Qi Yang

Publication date: 25 July 2008

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11937/7880

zbMATH Keywords

set valued map\(m\)th order adjacent derivative\(m\)th order adjacent set\(m\)th order optimality condition

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Optimality conditions for problems in abstract spaces (49K27)

Related Items (46)

Strict efficiency conditions for nonsmooth optimization with inclusion constraint under Hölder directional metric subregularity ⋮ On optimality conditions for quasi-relative efficient solutions in set-valued optimization ⋮ Second-order differential and sensitivity properties of weak vector variational inequalities ⋮ Generalized Higher-Order Optimality Conditions for Set-Valued Optimization under Henig Efficiency ⋮ Higher order optimality conditions for Henig efficient solutions in set-valued optimization ⋮ Higher-order optimality conditions in set-valued optimization using radial sets and radial derivatives ⋮ Quasi-contingent derivatives and studies of higher-orders in nonsmooth optimization ⋮ Variational sets of perturbation maps and applications to sensitivity analysis for constrained vector optimization ⋮ New higher-order strong Karush-Kuhn-Tucker conditions for proper solutions in nonsmooth optimization ⋮ On necessary optimality conditions with higher-order complementarity slackness for set-valued optimization problems ⋮ On second-order proto-differentiability of perturbation maps ⋮ Strong Fermat rules for constrained set-valued optimization problems on Banach spaces ⋮ Higher-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization with nonsolid ordering cones ⋮ Second-order optimality conditions for strict efficiency of constrained set-valued optimization ⋮ Second-order differentiability of generalized perturbation maps ⋮ Higher-Order Karush--Kuhn--Tucker Conditions in Nonsmooth Optimization ⋮ Higher-order weakly generalized epiderivatives and applications to optimality conditions ⋮ Higher-order optimality conditions for weakly efficient solutions in nonconvex set-valued optimization ⋮ Unnamed Item ⋮ Second-order optimality conditions for set-valued optimization problems under Benson proper efficiency ⋮ Higher-order Mond-Weir duality for set-valued optimization ⋮ New higher-order weak lower inner epiderivatives and application to Karush-Kuhn-Tucker necessary optimality conditions in set-valued optimization ⋮ Second-Order Composed Radial Derivatives of the Benson Proper Perturbation Map for Parametric Multi-Objective Optimization Problems ⋮ Second-order lower radial tangent derivatives and applications to set-valued optimization ⋮ On higher-order mixed duality in set-valued optimization ⋮ Duality and its applications to optimality conditions with nonsolid cones ⋮ New second-order tangent epiderivatives and applications to set-valued optimization ⋮ Existence and boundedness of second-order Karush-Kuhn-Tucker multipliers for set-valued optimization with variable ordering structures ⋮ Second-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization subject to mixed constraints ⋮ Second-Order Optimality Conditions for Set-Valued Vector Equilibrium Problems ⋮ Second-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization ⋮ Higher-order optimality conditions for proper efficiency in nonsmooth vector optimization using radial sets and radial derivatives ⋮ Sensitivity and stability for the second-order contingent derivative of the proper perturbation map in vector optimization ⋮ Sequential optimality conditions for fractional optimization with applications to vector optimization ⋮ Higher order weak epiderivatives and applications to duality and optimality conditions ⋮ New second-order radial epiderivatives and nonconvex set-valued optimization problems ⋮ Higher-order optimality conditions and duality for approximate solutions in non-convex set-valued optimization ⋮ A new nonlinear scalarization function and applications ⋮ Second-Order M-Composed Tangent Derivative and Its Applications ⋮ Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality ⋮ Characterizations of Approximate Duality and Saddle Point Theorems for Nonsmooth Robust Vector Optimization ⋮ A note on ``Higher-order generalized Studniarski epiderivative and its applications in set-valued optimization ⋮ Second-order weakly composed adjacent-generalized contingent epiderivatives and applications to composite set-valued optimization problems ⋮ Higher-order weakly generalized adjacent epiderivatives and applications to duality of set-valued optimization ⋮ Second-order composed contingent epiderivatives and set-valued vector equilibrium problems ⋮ Higher-order optimality conditions for set-valued optimization with ordering cones having empty interior using variational sets

Cites Work

• Unnamed Item
• Weak Pareto-optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space
• Maximal vectors and multi-objective optimization
• Optimality conditions for vector mathematical programming via a theorem of the alternative
• Second-order optimality conditions in multiobjective optimization problems
• \(K\)-epiderivatives for set-valued functions and optimization
• Nonconvex vector optimization of set-valued mappings.
• Second order necessary conditions in set constrained differentiable vector optimization
• Second-order optimality conditions in set optimization
• Optimality conditions in differentiable vector optimization via second-order tangent sets
• First-order optimality conditions in set-valued optimization
• Contingent derivatives of set-valued maps and applications to vector optimization
• An Existence Theorem in Vector Optimization
• A multiplier rule in set-valued optimisation
• GENERALIZED CONTINGENT EPIDERIVATIVES IN SET-VALUED OPTIMIZATION: OPTIMALITY CONDITIONS
• Optimality conditions for maximizations of set-valued functions
• Set-valued analysis

This page was built for publication: Higher-order optimality conditions for set-valued optimization